{"paper":{"title":"On dimension growth of modular irreducible representations of semisimple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ivan Losev, Roman Bezrukavnikov","submitted_at":"2017-08-04T05:53:59Z","abstract_excerpt":"In this paper we investigate the growth with respect to $p$ of dimensions of irreducible representations of a semisimple Lie algebra $\\mathfrak{g}$ over $\\overline{\\mathbb{F}}_p$. More precisely, it is known that for $p\\gg 0$, the irreducibles with a regular rational central character $\\lambda$ and $p$-character $\\chi$ are indexed by a certain canonical basis in the $K_0$ of the Springer fiber of $\\chi$. This basis is independent of $p$. For a basis element, the dimension of the corresponding module is a polynomial in $p$. We show that the canonical basis is compatible with the two-sided cell "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01385","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}